On the duality of aggregation operators and k-negations

In this paper we study a class of duality functions given by the solution of a system of functional equations related to the De Rham system. With the aid of a generalized dyadic representation system in the unit interval, we study a negation N which is a duality function for pairs of operators satisfying certain boundary conditions. New properties of N are investigated, including its singularity and fractal dimensions for several related sets. As an application we obtain an explicit expression for k-negations.

► We study a class of duality functions. ► A negation N that is a duality function for pairs of operators under boundary conditions is studied. ► Singularity of N and fractal dimensions for several related sets are investigated. ► An explicit expression for k-negations is obtained.